Question

perform the operation and simplify completely show all work. properties of expoenents/ super helpful property.

Answer 1

The rule of multiplication of the exponents is

$a^m.a^n=a^{m+n}$

We will use this rule with our question

$x^{\frac{5}{9}}.x^{\frac{2}{3}}$

We must add the fractions 5/9 and 2/3

To add fractions they must have the same denominators

Since the lowest common factor of 9 and 3 is 9, then

$\frac{5}{9}+\frac{2}{3}=\frac{5}{9}+\frac{2\times3}{3\times3}=\frac{5}{9}+\frac{6}{9}=\frac{11}{9}$

Then the expression is

$x^{\frac{5}{9}}.x^{\frac{2}{3}}=x^{\frac{5}{9}+\frac{2}{3}}=x^{\frac{11}{9}}$